Francisco A. M. Gomes, *A Sequential Quadratic Programming Algorithm with a Piecewise Linear
Merit Function*

**Abstract: **

A sequential quadratic
programming algorithm for solving nonlinear programming problems is presented.
The new feature of the algorithm is related to the definition of the merit function.
Instead of using one penalty parameter per iteration and increasing it as the
algorithm progresses, we suggest that a new point is to be accepted if it stays
sufficiently below the piecewise linear function defined by some previous
iterates on the $(f; ||C||^2_2)$ space. Therefore, the penalty parameter is
allowed to decrease between successive iterations. Besides, one need not to
decide how to update the penalty parameter. This approach resembles the filter
method introduced by Fletcher and Leyffer [7], but it is less tolerant since a
merit function is still used.

**KEY WORDS**: nonlinear programming, sequential
quadratic programming, merit functions.

**AMS 2000 Subject
Classification**: 65K05,
90C55, 90C30, 90C26

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May 11, 2004